The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 900 voters in the town and found that 75% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%. Determine the P-value of the test statistic. Round your answer to four decimal places.

Step-by-step explanation:

Null hypothesis: u = 0.72

Alternative hypothesis: u = / 0.72

Using the z score formula

z = p-P / √ (P (1-P) / n)

Where p (sample proportion) is 0.75, P (population proportion) is 0.72, and n = 900.

z = 0.75-0.72 / √ (0.72 (1-0.72) / 900)

z = 0.03/√ (0.72 (0.28) / 900)

z = 0.03/√ (0.2016/900)

z = 0.03 / √0.000224

z = 0.03/0.015

z = 2.0

To determine the p-value at an assumed significance level of 0.05 for a two tail test using a z score of 2, using the p value calculator, the p value is 0.0455.